Look at the warranties of all the other Samsung laptops. All say the same thing so you can bet yours is the same. The warranty on all of them starts on the date of purchase, not the date of delivery. Customer service would be happy to tell you about your specific model, I'm sure.
A tip: When you call, don't be belligerent and don't talk down to the rep even if his/her accent is so thick you can barely understand it. Just state the facts and ask your question plainly. After dealing with angry customers all day, the rep is usually so happy to have a rational, reasonable customer call that (s)he will usually give you better service. If they have to read from a script, let them. They're doing their job as best they can. Remember, the rep doesn't set the company policy and yelling at the person who may be your only means of getting a resolution is only counter-productive. I'm not talking to you or about Samsung specifically but it's a good general tip for anyone who needs support for a product. I've actually had support reps thank me for my lack of attitude and calm, reasonable manner on the phone. They went out of their way to help me.